Sources say bank executives are hoping the govenment stake will top out at about 25 percent, athough it is possible it could be as high as 40 percent. In either case, if the govenment converts its current preferred-stock status to common shares, Citi shareholders would see their stakes diluted and the government would potentially have a much larger influence over Citi.

Treasury spokesman Isaac Baker said: "We don’t comment on conversations with specific banks. However, as part of the Financial Stability Plan announced two weeks ago, financial institutions can apply to convert their existing preferred stock into a new convertible preferred stock, which can be exchanged into common equity shares at the option of the company as needed to strengthen their capital structure. We are open to considering a request to do so if the institution and it’s regulator believe it would promote the long term stability of that institution, and if we believe it’s in the best interest of long term stability of our economy and financial system."

Government's Stake in Citi

Citigroup is asking the government to convert a substantial portion of its $45B preferred shares into a new convertible stock. Insight with CNBC's Steve Liesman

"Citi's capital base is very strong and our Tier 1 capital ratio as measured at the end of the fourth quarter was 11.9%, among the highest in the industry," Citi said in a statement issued Sunday night. "We continue to focus and make progress on reducing the assets on our balance sheet, reducing expenses and streamlining our business for future profitable growth."

Comparing Citigroup's market capitalization with the number of preferred shares the government currently owns, if these shares were converted right now to common stock, they would worth more than 100 percent of Citi's total market capitalization.

Any additional money that Citi receives from the government automatically means a further stock dilution. While Obama Administration officials say this isn't nationalization, markets may interpret the situation differently and see it as de facto nationalization.

The move likely would make the U.S. government the biggest shareholder of Citigroup, owning a majority of its stock. This is de facto government ownership, or nationalization. What this ownership means at this point, nobody knows (See further discussion of this issue in the videos).

A Citigroup spokesman in Hong Kong declined to comment, but said in an emailed statement:"Citi's capital base is very strong and our Tier-1 capital ratio as measured at the end of the fourth quarter was 11.9 percent, among the highest in the industry.

Citi Edges Toward Uncle Sam

Whether Citibank is headed towards nationalization with the possibility of a greater government stake. Insight with CNBC's Charlie Gasparino

"We continue to focus and make progress on reducing the assets on our balance sheet, reducing expenses and streamlining our business for future profitable growth."

Citigroup officials also hope to persuade private investors that have bought preferred shares -- including the Government of Singapore Investment Corp., the Abu Dhabi Investment Authority and the Kuwait Investment Authority -- to also convert their preferred shares into common stock, the Wall Street Journal reported.

Citi could also try to raise fresh equity with a public share offering, the Financial Times reported. The aim would be to keep the government stake to no more than 40 percent or at least below 50 percent, it said, citing people familiar with the plan.

The Journal also reported that the Bank of America is not discussing a larger ownership stake for the U.S. government.

Citigroup stock had dropped below $2 on Friday for the first time since January 1991, buffeted by nationalization speculation. Citi stock has dropped 71 percent so far in 2009.